发表机构
Constructor University Bremen gGmbH（不来梅构造函数大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过引入一阶实现滤波器建模对抗性种群竞争，发现延迟预算不稳定性分为延迟诱导和滤波器诱导两种机制，并给出操作规则。
AI 中文摘要
我们建模了一个适应性竞赛，其中两个对抗性耦合的种群持续在竞争方法之间重新分配努力，但决策并非立即实施。每一方都有一个预期组合和一个部署组合：预期的重新分配遵循对对手的延迟观察，而部署则通过一阶实现滤波器跟随意图。在重心平衡和均匀探索下，线性化的标量分支具有一个特征因子，其中硬观察和部署延迟仅通过它们的总和进入，而实现速率通过不能被吸收到选择或探索中的实际滤波器因子进入。在严格对抗类中，负谱分支分为三个区域：弱分支没有正频率交叉，中间分支通过延迟诱导的Hopf分岔失去稳定性，强分支在零硬延迟时已经处于或超过实现滤波器不稳定裕度。这给出了一个操作性的延迟预算规则：在延迟诱导窗口中，减少任何硬延迟在起始点具有相同的一阶稳定杠杆；在滤波器诱导区域中，仅减少硬延迟无法恢复稳定性。平衡的标量性能可观测量通常显示均值偏移和两倍组成频率的二次谐波，在严格对抗下两个性能信号以固定幅度比反相锁定。对于基线分支，有限维Hopf规范形计算给出负三次系数，直接模拟再现了预测的阈值、幅度缩放和可观测量特征。激励应用包括网络安全和快速技术对抗适应。
英文摘要
Can two implementation processes with the same mean lag give opposite stability predictions for adaptive competition? We show that they can, and quantify the discrepancy. The motivating problem is technological coadaptation: decisions are revised while earlier changes are still being implemented and the competing system continues to change. Configuration updates in adaptive cyber defence and activation of revised algorithmic trading strategies provide concrete settings for this modelling question. A coupled replicator--mutator model separates intended portfolios from those actually in use. Near a uniform interior equilibrium, the interaction geometry determines the feedback branches; under strict antagonism, the largest singular value identifies the first unstable mode. For continuous implementation, hard observation and implementation lags enter through one delay budget. Replacing one smooth implementation filter by periodic partial updates, with zero hard lags and a uniform eligibility-phase calibration, preserves the mean waiting time but lowers the first gain boundary by an explicit positive quadratic correction for short release periods. A reproducible three-strategy benchmark exhibits decay under the continuous model and growth under periodic implementation at the same mean lag and interaction gain. Balanced performance observables can also understate the underlying portfolio oscillations. The results identify a concrete failure of mean-only timing descriptions and provide a benchmark for modelling adaptation and implementation separately.
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